Math & Statistics Calculators · Algebra
Free Linear Equation Calculator for One-Variable Equations, Slope, Intercepts, and Line Evaluation
Solve ax + b = c step by step, or work with y = mx + b to calculate intercepts, evaluate points, and compare the relationship between two lines.
Browser-basedNo sign-upPrivate local historyStep-by-step
Interactive calculator
Primary result—
X-intercept—
Y-intercept—
Enter equation values.
How to use it
- Choose equation-solving or line-analysis mode.
- For ax+b=c, enter coefficients a, b, and c.
- For y=mx+b, enter slope m, intercept b, and an x value.
- Calculate and inspect the substitution/isolation steps.
- Use the check line to verify the computed solution in the original equation.
What this calculator includes
1. Solve ax+b=cIsolate x step by step.
2. Degenerate casesIdentify no-solution and infinite-solution equations.
3. Slope-intercept modeWork directly with y = mx + b.
4. Evaluate yPlug in x to calculate a point.
5. X-interceptSolve y = 0.
6. Y-interceptReport b directly.
7. Point checkVerify a candidate point lies on the line.
8. Parallel comparisonCompare a second slope.
9. Perpendicular comparisonCheck m1×m2 = −1 when defined.
10. Step breakdownShow inverse operations clearly.
11. Local historySave solved equations.
12. Copy/downloadExport algebra work.
Result checklist
0 / 5 complete
Local calculation history
Formula and reference table
| Form | Key result | Formula |
|---|---|---|
| ax+b=c | Solution x | x = (c−b)/a |
| y=mx+b | y-intercept | (0,b) |
| y=mx+b | x-intercept | x = −b/m |
| Parallel lines | Equal slopes | m1 = m2 |
| Perpendicular lines | Negative reciprocal slopes | m1m2 = −1 |
Quick knowledge check
In y = mx + b, what does b represent?
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Frequently asked questions
What if a equals zero in ax+b=c?
Then the equation either has no solution or infinitely many solutions depending on whether b equals c.
How do I find an x-intercept?
Set y equal to zero and solve 0 = mx + b, giving x = −b/m when m is nonzero.
How can I tell if lines are parallel?
Distinct nonvertical lines are parallel when they have equal slopes.
Can this solve systems of equations?
This page focuses on one linear equation and single-line analysis, not full multi-equation systems.
Scope and accuracy
This calculator covers real-number linear equations and nonvertical slope-intercept lines. Vertical lines require forms such as x = constant and are not represented by finite m in y = mx + b.